Estimates on degenerate jump-diffusion processes and regularity of the related valuation equation

Many risk-neutral pricing problems proposed in the \ufb01nance literature require to be dealt with by solving the corresponding Partial Integro-Differential Equation. Unfortunately, neither the standard Sobolev spaces theory, or the present literature on viscosity solution theory is able to deal with some problems of interest in \ufb01nance. A recent result presented by Costantini, Papi and D\u2019Ippoliti accepted for pubblication on Finance and Stochastics [17], shows that, under general conditions on the coef\ufb01cients of the stochastic integro-differential equation, whenever a Lyapunov-type condition is satis\ufb01ed, the stochastic process does not reach the boundary of the domain where is de\ufb01ned. Furthermore, in the same work it has been proved that there exists a unique viscosity solution to the pricing problem when we deal with the corresponding pricing problem for European-type derivatives. The viscosity solution theory ensures just the continuity of the solution, when data are continuous, but does not guarantees that such a solution has some additional regularity. The aim of this work is to improve, for the pure differential case, the results existing in literature dealing with the regularity of both the solutions X of the underlying stochastic differential equations, and the solutions of the corresponding PDE. In particular we will provide some estimates related to dependence with respect to the initial data for the process X. Furthermore, dealing with the pricing problem, we improve our understanding on the assumptions that ensure the viscosity solution to have additional regularity properties beside the mere continuity. A Lipschitz-type dependence result with respect to initial data, until a stopping time \u3c4 , is shown whenever the coef\ufb01cients are locally Lipschitz continuous, and a Lyapunov-type condition is satis\ufb01ed. Such a result can be improved if a suitable weight function is put in place. A standard result in PDE theory ensures that, if the assumptions we assume in our work are satis\ufb01ed, then in each compact subset where the diffusion matrix is positive de\ufb01ned, there exists a unique classical solution to the localized problem if initial data are continuous (see e.g. [35] or [9]). We make use of such a result in order to prove that this classical solution coincides, in the same subset, with the unique viscosity solution found in [17]. We give an application of such results, applying our evidences to the stochastic volatility model proposed by Ekstrom and Tysk in [29]. In such a case all the hypotheses we are \ua8 currently assuming are satis\ufb01ed, and the expression of the Lyapunov function can be explicitely provided for different \ufb01nal payoff. As a consequence, we are able to get the results of the existence and uniqueness of a classical solution to the pricing problem presented in[29] in an independent way. Furthermore it is possible to consider weakened assumptions on the \ufb01nal payoff. On the other hand we try to consider a generalization of the model, allowing the process exhibits sudden jumps provided that the jump measure satis\ufb01es some suitable properties. In such a case, the expression for the Lyapunov function is provided as well, hence we are able to state that the considered valuation problem admits one and only one viscosity solution

HOMM. ICT for Hands on Multi Media Laboratories in Museums

AbstractProposal to develop HOMM: a prototype of ICT based tools for hands on multi-media activities in museums. Multidisciplinary teams will build specific contents of the application to support, test and evaluate it in a network of museums. Museums are identified as agents of economic and social development supporting lifelong learning

The spermatozoa caught in the net: the biological networks to study the male gametes post-ejaculatory life

<p>Abstract</p> <p>Background</p> <p>Mammalian spermatozoa, immediately after the ejaculation are unable to fertilize the oocyte. To reach their fertilizing ability the male gametes must complete a process of functional maturation, the capacitation, within the female genital tract. Only once the capacitation is completed the spermatozoa can respond to the oocyte interaction with the exocytosis of acrosome content, acrosome reaction (AR). These post-ejaculatory events are under the attention of Researchers from more than fifty years but their basic knowledge is still unsatisfactory. This failure could be due not to the insufficiency of available data, but to the inability to manage them in a descriptive model. Thus, to overlap this problem, the capacitation and the AR were represented using the biological networks formalism. In addition the effect of elimination from both the networks of the most linked (the hubs) or of random selected nodes was verified and the network representing the common element of capacitation and AR (C∩A) was realized.</p> <p>Results</p> <p>The statistical analysis of resulting graphs showed that capacitation, AR and C∩A networks follow the scale free topology and are characterized by low clustering. In all cases it was possible to identify the key molecules (Ca²⁺, ATP, P-Tyr, PKA, PLD1 in capacitation, Ca²⁺, ATP in AR and C∩A) and to describe their role in signalling transduction. The effect of hubs elimination caused the collapse of networks structure, while the elimination of random selected nodes did not affected it.</p> <p>Conclusions</p> <p>It was demonstrated that the post-ejaculatory life of male gametes is a series of events characterised by a high signalling efficiency and robustness against random failure. This strengthens the evidence that the adoption of biological networks modellization of capacitation and AR could increase the understanding of spermatozoa physiology, potentially opening new perspective in drug discovery, diagnosis and therapy of male infertility.</p

Estimates on degenerate jump-diffusion processes and regularity of the related valuation equation

Many risk-neutral pricing problems proposed in the finance literature require to be dealt with by solving the corresponding Partial Integro-Differential Equation. Unfortunately, neither the standard Sobolev spaces theory, or the present literature on viscosity solution theory is able to deal with some problems of interest in finance. A recent result presented by Costantini, Papi and D’Ippoliti accepted for pubblication on Finance and Stochastics [17], shows that, under general conditions on the coefficients of the stochastic integro-differential equation, whenever a Lyapunov-type condition is satisfied, the stochastic process does not reach the boundary of the domain where is defined. Furthermore, in the same work it has been proved that there exists a unique viscosity solution to the pricing problem when we deal with the corresponding pricing problem for European-type derivatives. The viscosity solution theory ensures just the continuity of the solution, when data are continuous, but does not guarantees that such a solution has some additional regularity. The aim of this work is to improve, for the pure differential case, the results existing in literature dealing with the regularity of both the solutions X of the underlying stochastic differential equations, and the solutions of the corresponding PDE. In particular we will provide some estimates related to dependence with respect to the initial data for the process X. Furthermore, dealing with the pricing problem, we improve our understanding on the assumptions that ensure the viscosity solution to have additional regularity properties beside the mere continuity. A Lipschitz-type dependence result with respect to initial data, until a stopping time τ , is shown whenever the coefficients are locally Lipschitz continuous, and a Lyapunov-type condition is satisfied. Such a result can be improved if a suitable weight function is put in place. A standard result in PDE theory ensures that, if the assumptions we assume in our work are satisfied, then in each compact subset where the diffusion matrix is positive defined, there exists a unique classical solution to the localized problem if initial data are continuous (see e.g. [35] or [9]). We make use of such a result in order to prove that this classical solution coincides, in the same subset, with the unique viscosity solution found in [17]. We give an application of such results, applying our evidences to the stochastic volatility model proposed by Ekstrom and Tysk in [29]. In such a case all the hypotheses we are ¨ currently assuming are satisfied, and the expression of the Lyapunov function can be explicitely provided for different final payoff. As a consequence, we are able to get the results of the existence and uniqueness of a classical solution to the pricing problem presented in[29] in an independent way. Furthermore it is possible to consider weakened assumptions on the final payoff. On the other hand we try to consider a generalization of the model, allowing the process exhibits sudden jumps provided that the jump measure satisfies some suitable properties. In such a case, the expression for the Lyapunov function is provided as well, hence we are able to state that the considered valuation problem admits one and only one viscosity solution.Many risk-neutral pricing problems proposed in the finance literature require to be dealt with by solving the corresponding Partial Integro-Differential Equation. Unfortunately, neither the standard Sobolev spaces theory, or the present literature on viscosity solution theory is able to deal with some problems of interest in finance. A recent result presented by Costantini, Papi and D’Ippoliti accepted for pubblication on Finance and Stochastics [17], shows that, under general conditions on the coefficients of the stochastic integro-differential equation, whenever a Lyapunov-type condition is satisfied, the stochastic process does not reach the boundary of the domain where is defined. Furthermore, in the same work it has been proved that there exists a unique viscosity solution to the pricing problem when we deal with the corresponding pricing problem for European-type derivatives. The viscosity solution theory ensures just the continuity of the solution, when data are continuous, but does not guarantees that such a solution has some additional regularity. The aim of this work is to improve, for the pure differential case, the results existing in literature dealing with the regularity of both the solutions X of the underlying stochastic differential equations, and the solutions of the corresponding PDE. In particular we will provide some estimates related to dependence with respect to the initial data for the process X. Furthermore, dealing with the pricing problem, we improve our understanding on the assumptions that ensure the viscosity solution to have additional regularity properties beside the mere continuity. A Lipschitz-type dependence result with respect to initial data, until a stopping time τ , is shown whenever the coefficients are locally Lipschitz continuous, and a Lyapunov-type condition is satisfied. Such a result can be improved if a suitable weight function is put in place. A standard result in PDE theory ensures that, if the assumptions we assume in our work are satisfied, then in each compact subset where the diffusion matrix is positive defined, there exists a unique classical solution to the localized problem if initial data are continuous (see e.g. [35] or [9]). We make use of such a result in order to prove that this classical solution coincides, in the same subset, with the unique viscosity solution found in [17]. We give an application of such results, applying our evidences to the stochastic volatility model proposed by Ekstrom and Tysk in [29]. In such a case all the hypotheses we are ¨ currently assuming are satisfied, and the expression of the Lyapunov function can be explicitely provided for different final payoff. As a consequence, we are able to get the results of the existence and uniqueness of a classical solution to the pricing problem presented in[29] in an independent way. Furthermore it is possible to consider weakened assumptions on the final payoff. On the other hand we try to consider a generalization of the model, allowing the process exhibits sudden jumps provided that the jump measure satisfies some suitable properties. In such a case, the expression for the Lyapunov function is provided as well, hence we are able to state that the considered valuation problem admits one and only one viscosity solution.LUISS PhD Thesi

Cumulus cells steroidogenesis is influenced by the degree of oocyte maturation

BACKGROUND: The possibility to predict the ability of a germ cell to properly sustain embryo development in vitro or in vivo as early as possible is undoubtedly the main problem of reproductive technologies. To date, only the achievement of nuclear maturation and cumulus expansion is feasible, as all the studies on cytoplasmic maturation are too invasive and have been complicated by the death of the cells analyzed. The authors studied the possibility to test the cytoplasmic quality of pig oocytes by evaluating their ability to produce steroidogenesis enabling factor(s). To this aim, oocytes matured under different culture conditions that allowed to obtain gradable level of cytoplasmic maturation, were used to produce conditioned media (OCM). The secretion of the factor(s) in conditioned media was then recorded by evaluating the ability of the spent media to direct granulosa cells (GC) steroidogenesis. METHODS: In order to obtain germ cells characterized by a different degree of developmental competence, selected pig oocytes from prepubertal gilts ovaries were cultured under different IVM protocols; part of the matured oocytes were used to produce OCM, while those remaining were submitted to in vitro fertilization trials to confirm their ability to sustain male pronuclear decondensation. The OCM collected were finally used on cumulus cells grown as monolayers for 5 days. The demonstration that oocytes secreted factor(s) can influence GC steroidogenesis in the pig was confirmed in our lab by studying E(2 )and P(4 )production by cumulus cells monolayers using a radioimmunoassay technique. RESULTS: Monolayers obtained by growing GC surrounding the oocytes for five days represent a tool, which is practical, stable and available in most laboratories; by using this bioassay, we detected the antiluteal effect of immature oocytes, and for the first time, demonstrated that properly matured germ cells are able to direct cumulus cells steroidogenesis by inhibiting E(2 )production (P < 0.01). Nevertheless, only fully competent oocytes were able to suppress estrogens production, while those cultured under unfavourable conditions were unable to exert any inhibitory effect on the functions of cumulus cells (P < 0.01). CONCLUSION: These results demonstrated that good quality oocytes can be easily selected on the basis of their ability to affect granulosa cell steroidogenesis thus reducing failures in reproductive technologies due to the transfer of fertilized oocytes with a scarce ability to sustain embryo development

Networks Models of Actin Dynamics during Spermatozoa Postejaculatory Life: A Comparison among Human-Made and Text Mining-Based Models

Here we realized a networks-based model representing the process of actin remodelling that occurs during the acquisition of fertilizing ability of human spermatozoa (HumanMade_ActinSpermNetwork, HM_ASN). Then, we compared it with the networks provided by two different text mining tools: Agilent Literature Search (ALS) and PESCADOR. As a reference, we used the data from the online repository Kyoto Encyclopaedia of Genes and Genomes (KEGG), referred to the actin dynamics in a more general biological context. We found that HM_ALS and the networks from KEGG data shared the same scale-free topology following the Barabasi-Albert model, thus suggesting that the information is spread within the network quickly and efficiently. On the contrary, the networks obtained by ALS and PESCADOR have a scale-free hierarchical architecture, which implies a different pattern of information transmission. Also, the hubs identified within the networks are different: HM_ALS and KEGG networks contain as hubs several molecules known to be involved in actin signalling; ALS was unable to find other hubs than “actin,” whereas PESCADOR gave some nonspecific result. This seems to suggest that the human-made information retrieval in the case of a specific event, such as actin dynamics in human spermatozoa, could be a reliable strategy

Effect of Estradiol and Progesterone on ovine Amniotic Epithelial Cells

This study was designed to clarify Estradiol (E2) and Progesterone (P4) steroid effects on ovine Amniotic Epithelial Cells (oAECs) that has a conserved plasticity and highly self-renewable capacity (Parolini et al., Stem Cells, 26(2), 300–311, 2008; Barboni et al., Stem Cell Rev Rep, 10:725–741, 2014). Based on their conserved immunomodulatory properties, oAECs are suitable for allo and xeno-transplantation (Barboni et al., Cell Transplant, 21(11), 2377–2395, 2012; Muttini et al., Res Vet Sci, 94(1),158–169, 2013). To date, no information is present on the effects of prolonged steroid exposition on AECs. oAECs were cultured as previously reported (Barboni et al., Cell Transplant. 21(11), 2377–2395, 2012) and treated with 12.5μM and 25μM of E2 or P4 (Sigma-Aldrich, Milan, Italy), alone and in both combinations, for three passages. Untreated cells were marked control (CTR). At 70% confluency, cells were detached for doubling time (DT) evaluation. Cells at fourth passage were differentiated for 21 days in osteogenic media (DM) (Mattioli et al., Cell Biol Int 36(1):7-19, 2012) without steroid. Alizarin Red and Alcian-Blue (Sigma-Aldrich, Milano, Italy) stainings were performed. RNA and cDNA were obtained as previously reported (Barboni et al., Cell Transplant. 21(11), 2377–2395, 2012). Real Time for NANOG, SOX2 ,OCT4 stemness genes expression were performed by SensiFast SYBR (Bioline, Aurogene, Rome, Italy) using specific primers (Mattioli et al., Cell Biol Int. 36(1):7-19, 2012).The protocol was: 5 min at 95°C, 30 cycles at 95°C for 15 sec, 60°C for 30 sec, 72°C for 15 sec. Comparative Ct 2-ΔΔC(t) normalization to GAPDH was applied. IHC analyses were carried out for Cytokeratin 8 and αSMA expression as previously reported (Barboni et al. PLoS ONE 7(2): e30974, 2012). Data expressed as mean (±SD), compared by one-way ANOVA followed by Tukey’s test (GraphPad Prism 5). Significant values for P &lt; 0.05. Steroids treated ovine AECs proliferate with significant differences between concentrations. While P4 treated cells showed cuboidal shape and Cytokeratin expression until third passage, CTR and E2 treated cells showed a rapid downregulation of Cytokeratin and increased αSMA expression. oAECs with E2+P4 showed both cell type morphology. Steroids modified stemness genes based on the concentration. 12.5 μM E2, 25μM P4 and 25μM of both E2+P4 treatments maintained higher OCT4, NANOG and SOX2 expressions in treated cells despite their progressive downregulation in the CTR. Moreover, compared to CTR, after Alizarin staining, steroid pretreated cells suffered morphological changes under DM acquiring Alcian Blue-positive chondrogenic-like morphology. AECs stemness properties and plasticity can be modified by prolonged steroidal treatment. These data improve our knowledge, opening new prospective on oAEC use in stem cell-based therapy. Acknowledgments. Research supported by H2020-MSCA ITN EJD-REP BIOTECH 675526